Application to summer precipitation recorded in Montréal, QC

In this section, we show that the EGP model based on the truncated Beta distribution can be used to model non-zero precipitation, which corresponds to exceedances above the very low threshold of 0, while maintaining the tail behavior.

Data

The daily summer precipitation (May–October) recorded at the Montréal-Trudeau International Airport meteorological station (Québec, Canada) from 2000 to 2020 are investigated. This dataset can be loaded using the ExtendedExtremes.dataset provided for this tutorial.

data = ExtendedExtremes.dataset("pcp")
filter!(row -> row.Date>= Date(2000,1,1), data)
filter!(row -> month(row.Date) in 5:10, data)
dropmissing!(data)
first(data,5)

Modeling the non-zero precipitation

The EGP parameter estimation with maximum likelihood is performed with the fit_mle function.

u = 0.0
y = data.pcp[data.pcp .> u] .- u;

fd = fit_mle(ExtendedGeneralizedPareto{TBeta}, y)

ExtendedGeneralizedPareto{TBeta{Float64}}(
V: TBeta{Float64}(α=0.03797646874817642)
G: GeneralizedPareto{Float64}(μ=0.0, σ=11.75360977328577, ξ=-0.01981634739270602)
)

Several diagnostic plots for assessing the accuracy of the EGP model fitted to the Montréal data are can be shown with the diagnosticplots function:

set_default_plot_size(16cm, 16cm)
ExtendedExtremes.diagnosticplots(y, fd)